# Mixture Toxicity Prediction Using GCA (General) Predict the mixture toxicity based on individual concentration-response information. Thirteen monotonic(sigmoidal) models ("Hill", "Hill_two", "Hill_three", "Hill_four", "Weibull", "Weibull_three", "Weibull_four", "Logit", "Logit_three", "Logit_four", "BCW(Box-Cox-Weibull)", "BCL(Box-Cox-Logit)", "GL(Generalized Logit)") are incorporated to construct the GCA equation. The dichotomy technique is used to solve the constructed equation. Three optional mixture design methods are provided. One is the arbitrary concentration ratio (acr) for mixture components. Users can arbitrarily deign a random ratio for each component in the mixture. Other two options are equal effect concentration ratio (eecr) and uniform design concentration ratio (udcr). ```r gcaPred(model, param, mixType, effv, refEffv, rtype, lb, ub, sav = FALSE) ``` ## Arguments - `model`: vector of equation names - `param`: numeric matrix of fitting coefficients with rownames (equation selected) and colnames (ALpha, Beta, and Gamma). For equations with two parameters, Gamma can be set as zero or any other numeric value. - `mixType`: experimental design of the mixture. acr: arbitrary concentration ratio; eecr: equal effect concentration ratio; udcr: uniform design concentration ratio. - `effv`: numeric vector with single or multiple (scaled) effect values (0 ~ 1). - `refEffv`: to determine the concentration ranges for predicting effect. Use scaled values (0 ~ 1). - `lb`: lower bound for solving constructed IA using diochotomy method (default is 1E-9). - `ub`: upper bound bound for solving constructed IA using diochotomy method(default is 9). - `rtype`: the response type of endpoint: 'continuous' or 'quantal' data. - `sav`: TRUE: save output to a default file; FALSE: output will not be saved; a custom file directory: save output to the custom file directory. ## Details The generalized concentration addition (GCA) model was proposed by Howard and Webster to predict mixtures containing partial agonists (Howard and Webster, 2009). $$ \sum\limits_{i = 1}^n {\frac{{{c_i}}}{{f_i^{ - 1}\left( E \right)}}} = 1 $$ Empirical data were used to fit concentration-response function, and then predict the mixture response using the inverse function. Previous studies used Hill_two function to fit individual concentration response curves in the GCA prediction (Hadrup et al., 2013; Howard et al., 2010). Here, we incorporated thirteen functions to construct the GCA equation and the dichotomy technique is used to solve the constructed equation. ## Returns - **x**: a series of concentrations - **e**: a series of effects caused by the concentrations (x) as predicted by gca - **pct**: the concentration ratio (percent) of every component in the mixture - **uniTab**: the uniform design table used to construct the mixture when mixType is udcr ## References Howard, G.J., Schlezinger, J.J., Hahn, M.E., Webster, T.F., 2010. Generalized Concentration Addition Predicts Joint Effects of Aryl Hydrocarbon Receptor Agonists with Partial Agonists and Competitive Antagonists. Environ. Health Perspect. 118, 666-672. Howard, G.J., Webster, T.F., 2009. Generalized concentration addition: A method for examining mixtures containing partial agonists. J. Theor. Biol. 259, 469-477. ## See Also `gcaHill` ## Examples ```r ## example 1 # using GCA to predict the mixtures designed by equal effect concentration ratio (eecr) at the # effect concentration of EC50 # the eecr mixture design is based on seven antibiotics(seven factors). model <- antibiotox$sgl$model param <- antibiotox$sgl$param refEffv <- c(0.1, 0.50, 0.80) gcaPred(model, param, mixType = "eecr", effv = 0.5, refEffv, rtype = 'quantal') ## example 2 # using GCA to predict the mixtures designed by uniform design concentration ratio (udcr) # the udcr mixture design is based on 2 antibiotics(2 factors) and # three levels (EC05, EC20, and EC50 ) model <- antibiotox$sgl$model[1 : 2] param <- antibiotox$sgl$param[1 : 2, ] effv <- c(0.05, 0.20, 0.50) refEffv <- c(0.1, 0.80) gcaPred(model, param, mixType = "udcr", effv, refEffv, rtype = 'quantal') ## example 3 # using GCA to predict the mixtures designed by arbitrary concentration ratio (acr) # the udcr mixture design is based on 2 heavy metals (2 factors). # the every component in the mixture shares exactly the same ratio (0.5) model <- cytotox$sgl$model[1 : 2] param <- cytotox$sgl$param[1 : 2, ] effv <- c(0.5, 0.5) refEffv <- c(0.1, 0.80) gcaPred(model, param, mixType = "acr", effv, refEffv, rtype = 'quantal') ```

gcaPred function